Clifford and Sam each have some game cards. If Clifford gives Sam 48 game cards they both will have an equal number of game cards. If Clifford gives Sam 112 game cards, Clifford will have 1/3 as much as Sam. How many game cards does Clifford have at first?
Let C be the number of game cards Clifford has at first and S be the number of game cards Sam has at first.
First, we know that C - 48 = S + 48 and C + 112 = S/3.
So S = C - 96 and S = 3C - 112.
Thus C - 96 = 3C - 112.
Thus 3C - C = 112 - 96
Thus 2C = 16
Thus C = <<8=8>>8. Answer: \boxed{8}.
Let's say Clifford has x game cards at first.
According to the given information, if Clifford gives Sam 48 game cards, they will have an equal number of game cards. So, after this transfer, Clifford will have (x - 48) game cards and Sam will have (x + 48) game cards.
If Clifford gives Sam 112 game cards, Clifford will have 1/3 as much as Sam. So, after this transfer, Clifford will have (x - 112) game cards and Sam will have (3 * (x - 112)) game cards.
Now let's set up the equation based on the information given:
(x - 48) = (3 * (x - 112))
Simplifying the equation:
x - 48 = 3x - 336
Adding 336 to both sides:
x + 288 = 3x
Subtracting x from both sides:
288 = 2x
Dividing both sides by 2:
x = 144
Therefore, Clifford has 144 game cards at first.